The use of electronic health (eHealth) technologies in healthcare improves the quality of health services furnished to patients. The application of these technologies helps physicians and other health professionals to pursue early detection of abnormal status on patients' health. Body sensor networks are a type of wireless sensor networks aimed to be deployed on persons in order to collect physiological parameters for healthcare monitoring purposes. These BSNs are composed by several small sensors placed along patient's body, and capable to send (wirelessly) the collected health parameters to remote providers. BSNs need to operate every time and everywhere to transmit these important parameters to healthcare providers or automatic system to detect any anomaly in the patient health status. To provide this continuous monitoring of patients, it is mandatory to provide mobility support for the BSN so it can always be connected to some gateway to the Internet and therefore to back-end health providers. Several mechanisms with mobility support for mobile devices have been provided. However, the mobility support of a whole BSN has not been fully addressed. This article overviews available handover mechanisms used for wireless sensors mobility and proposes a new ubiquitous mobility approach for BSNs in healthcare. A case study with this new handover mechanism developed for a hospital infirmary is presented and highlights the gain of performances of the proposed solution.